"junoexpress" <mathimagical@netscape.net> wrote in messagenews:1139416665.163490.311850@o13g2000cwo.googlegroups.com...> Hi,>> I am curious if there is a general way to understand the solution to> the following (simple) complex analysis problem.>> Suppose we have an n-dimensional vector space, and a fixed (i.e. known)> vector x in C^n.>> The question is whether there is a way to describe the set of all> vectors z such that:> (i) z' * x = 1> (where ' denotes conjugate transpose).>> If you sketch out this problem, it is not difficult to see that the> conditions:> (ii.a) Re(z' * x) = 1> and> (ii.b) Im(z' * x) = 0> give you two linear equations in 2n unknowns, which you could then> solve (in a least squares sense).>> This method of analysis, however, does little to describe what the> solution set is like. I am curious if anyone else has another way of> thinking about this problem. More general pictures for how to visualize> this condition (like as a projection for example) do not seem that easy> to conjur up.>> Thank you for any help you can provide,>> Juno>